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Football fans will want to pay their respects to the brilliant Ajax club at their impressive new stadium, Amsterdam ArenA. Visit the interactive museum, which brings the club and its greatest moments to life, and tour the state-of- the- art 50,000-seat stadium. There are usually six tours a day in summer, four in winter, except on event days; phone ahead for times.

This welcome green space to the south of the city has a rose garden, a maze and an art gallery for adults, as well as pony rides, farm animals and a miniature steam train for children. Best of all, at the southernmost tip of the park, is the well-preserved De Rieker windmill. Built in 1636, it was a favourite of Rembrandt, whose statue stands nearby. Now a private home.

This museum of modern art in residential Amstelveen is dedicated in part to the influential Dutch movement conceived in 1948. Its founders, including Dutchman Karel Appelamalgamated the names of their home cities – Copenhagen, Brussels and Amsterdam – to create its name: CoBrA. They wanted to promote art that was spontaneous and inclusive, and were inspired by the work of primitives, children and the mentally ill. Paintings in the permanent collection are shown in changing thematic displays, augmented by temporary exhibitions. The light, spare building, by Wim Quist, opened in 1995.

A housing estate seems an unlikely tourist attraction, but the complex built for the De Dageraad (Dawn) housing association from 1918–23 is well worth a visit – especially for anyone interested in the Amsterdam School of Architecture. Piet Kramer and Michel de Klerk designed sculptural buildings of great originality, with tiled roofs that undulate in waves, and brick walls that billow and curve. The project was part of an initiative chargeto provide better housing for poorer families, in the wake of the revolutionary Housing Act of 1901.

The elegant Louis XIV-style Frankendael is the last survivor of an enclave of exclusive early 18th-century houses, which were built south of Plantage Middenlaan on reclaimed land called the Watergraafsmeer. Although closed to the public, the ornamented façade and the fountain, made by Ignatius van Logteren, are worth seeing. However, the rear gardens are open to the public, and offer a peaceful – if slightly untidy and overgrown – refuge of shrubs and ancient trees.

These former docks, outposts of the Eastern Islands, have been the subject of intense development and renovation in the last decade, in response to the city’s need for new housing. They are now considered trendy places to live, and designer home shops, boutiques, restaurants and cafés are springing up. They are most easily reached by the two bridges from Oostelijke Handelskade.

The most arresting feature of this interactive science and technology centre – the largest in the Netherlands – is the building itself. Designed by Renzo Piano, its harbour location (in the Eastern Islands) gave the impetus for a green copper structure resembling a vast ship. The great views from the top deck will certainly appeal, even if the hands-on games, experiments and demonstrations, designed to entertain and educate both children and adults, do not.